Can one be Jewish and not believe in God?

As the Talmud states "Yisroel af al pi shechata, yisroel hu" Meaning an Israelite remains so despite any sinning or renunciation. A Jew is born Jewish and can NEVER forfeit that status. Thus, Disbelief in God cannot undo one's innate Jewish identity. Nor can a Jewish Apostate - one who converts to another faith - ever undo their natural born Judaism. *

And so personally, I treat Jewish Non-believers who become Professing Atheists as "Full Apostate Jews" They have the same status as any Jew who converts to any another religion. A Jewish Buddhist or a Jewish Athheist, either way is still an Israelite.

Now let's rephrase this query to address "Orthodoxy" - Can one still be an Orthodox Jew and not believe in God?

One expects a resounding NO! I choose to give a more nuanced answer It's axiomatic that Orthodox Jews are required to Believe in God, or preferably to "KNOW God" which is the superior translation of the Rambam (Rabbi Moses Ben Maimon, also called Maimonides) in several places. However, this requirement does not necessarily presuppose that one STARTS from a position of firm belief. "Not at all," say I. One may start from inner doubt or even agnosticism

This sets up at least these two caveats

An Orthodox Jew may indeed express doubt., but not denial of God. An Orthodox Jew is deviating from basic Judaism if/when he professes disbelief as outlined EG by Maimonides 13 articles, or by Albo's 3 Fundamentals

Second an Orthodox Jew is obligated to KNOW God. This is clear from the aforementioned writings of Rambam [EG Hilchot Yesodei Hatorah and Rabbi AJ Heschel "God in Search of Man"] Despite any misgivings or inner doubts, an Orthodox Jew must take steps to Seek and Find God. This mitzvah [commandment] is indispensable.

Summary:

A born Jew is always a Jew despite one's beliefs, disbeliefs, or even apostasies.

An Orthodox Jew is required to Believe in God. However, if one starts from a position of doubt, it is legitimate to then begin the journey to discover God and eventually to Know God.

Some Sources for further Research:

Talmud Bavli 47b
"If one immersed - behold he is like an Israelite for every matter. How is this halakhah applied? If he returns [to practice idolatry], after he married an Israelite woman, he is considered Israel-mumar, however their marriage stands. [Despite his renunciation]

Talmud Bavli qiddushin 36a R Meir says "either way you are called Children ... And when they worship idols they are NOT Children [of the Lord]?" -Rambam Hilchot T'shuva Ch. 3 regarding apostates and their repentance

Here is a Link to in-depth research on the status of Apostates in Halachah:

Yes, a person is Jewish not simply by virtue of belief but of choosing a Jewish life through conversion or being born as a Jew. However, there is an important difference between being Jewish and living Jewishly.

Judaism asks us to uphold certain standards of practice and belief, so though you do not somehow automatically leave the Jewish people by your belief or practice certain beliefs and practice challenge some basic Jewish assumptions. One of those assumptions is a belief in an overarching power, a thread which connects all creation to a single source. We call this single source God in English, because we, as human beings need to assign language to belief. This belief of oneness, a connecting force in the world is a fundamental Jewish belief and underlies much of our practice, from the Calendar year to the commandments to bring greater justice to the world, to ritual observance. Underlying all of these behaviors which are essential to living a Jewish life is the idea that we are all connected to each other, the world, a power beyond our understanding and even beyond our imagination. God, if you will, in Judaism is an ever changing entity not the "man" on high you might have learned about in school judging from above. God in this Jewish conception is a part of the ongoing process of creation woven into the fabric of human existence.

So yes, of course you can be Jewish and not believe in God - because being Jewish literally is simply a definition of your birth or your conversion but living Jewishly is a whole different story and is all about how you act, what you believe and the connection to a higher power woven into the fabric of your very world.

I found that this same question has already been answered on the website by four of my colleagues. Rabbis Rosenberg, Rothstein, Schwab, and Wolpoe have each answered this question. Rabbi Wolpoe’s answer is attached to this question, while the other three responses appear on the site, accessible at the following URL:

THE VIEWS EXPRESSED IN ANSWERS PROVIDED HEREIN ARE THOSE OF THE INDIVIDUAL JVO PANEL MEMBERS, AND DO NOT
NECESSARILY REFLECT OR REPRESENT THE VIEWS OF THE ORTHODOX, CONSERVATIVE OR REFORM MOVEMENTS, RESPECTIVELY.